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QUANTUM FEATURES OF HARMONIC OSCILLATORS: INVESTIGATING THE LIMITS OF QUANTUM MECHANICS

LUCA ABRAHAO PAIVA

Published Oct 4, 2024• 0 citations
Publisher

Abstract

Nothing is achieved alone.I am what and where I am because of all of those who crossed my path.Without all the good and the bad, I would not be here.I want to deeply thank all of those who joined me in this amazing experience.More specifically... To my mother who have always supported me in every decision I made, who let me walk on my own, but made me sure she was always there for what I needed.To my father, that always taught me the value of education and dedication.To my brother, to all the coffee and many gestures of love and appreciation.I hope I can inspire you, the same way you inspire me.À minha avó, que não somente me ensinou a ler, mas também com quem aprendi muito sobre amor, família e perseverança.To my friends who have been with me throughout all these years, sharing dreams, wins, loses but always there for each other.Specifically, those who started with me this journey in Physics, Rafael e Vitória, and are a fundamental part of my trajectory.Also, all my colleagues from the Quantum Adventures group, that quickly became a second family.To my friend and advisor, Thiago.It was out of pure chance I ended up in that interview and sent you an email.Now, two years later, I can see the difference it has made and how much you helped me through all of it, not only academically.It was a pleasure share these last two years.And hopefully, many to come. At last, I want to thank my beloved girlfriend Clara.There is no overstating the importance you have in my life.A great part of what I am, is due to you.And that part is certainly the best of me.Love you dearly.

DOI
10.17771/pucrio.acad.68634

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Nothing is achieved alone.I am what and where I am because of all of those who crossed my path.Without all the good and the bad, I would not be here.I want to deeply thank all of those who joined me in this amazing experience.More specifically... To my mother who have always supported me in every decision I made, who let me walk on my own, but made me sure she was always there for what I needed.To my father, that always taught me the value of education and dedication.To my brother, to all the coffee and many gestures of love and appreciation.I hope I can inspire you, the same way you inspire me.À minha avó, que não somente me ensinou a ler, mas também com quem aprendi muito sobre amor, família e perseverança.To my friends who have been with me throughout all these years, sharing dreams, wins, loses but always there for each other.Specifically, those who started with me this journey in Physics, Rafael e Vitória, and are a fundamental part of my trajectory.Also, all my colleagues from the Quantum Adventures group, that quickly became a second family.To my friend and advisor, Thiago.It was out of pure chance I ended up in that interview and sent you an email.Now, two years later, I can see the difference it has made and how much you helped me through all of it, not only academically.It was a pleasure share these last two years.And hopefully, many to come. At last, I want to thank my beloved girlfriend Clara.There is no overstating the importance you have in my life.A great part of what I am, is due to you.And that part is certainly the best of me.Love you dearly.
I would like to thank my advisor, Michael Cross, for his mentorship. I learned from him how to ask basic questions when doing research, as well as how to articulate the results in a paper or talk. I appreciate that I could always drop by to ask questions about any kind of physics. I also appreciate the freedom I had to work on some admittedly random problems. Next, I would like to thank Gil Refael for teaching me a lot of new physics and broadening my horizons. In addition, I want to thank Hartmut Häffner, to whom I owe my knowledge of quantum optics. Thanks also to Harvey Newman for his support during college. I would also like to acknowledge the people that I have had the pleasure of discussing
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com apoio da Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brasil.Processos nº 2022/01421-9 e nº 2022/14069-1.Eu agradeço muito pelo suporte financeiro, que me permitiu atender eventos importantes do meu campo de pesquisa e a fazer um intercâmbio inesquecível.iv I would first like to thank my advisor, Bárbara Amaral.Her guidance over these almost four years of undergraduate and master's studies has been essential to my development as a student and researcher.Thank you for all your patience, for giving me so many incredible opportunities, and for showing me that it is possible to do physics without giving up on other important aspects of life.Thank you for being an incredible person, in whom I draw inspiration.I hope to continue learning a lot from you and gossiping over coffee breaks at conferences and IFQIFs.To my parents, Maria de Fátima and Jones, who are my foundation and the loves of my life.I am immensely grateful for all the support you have given me.This work is largely the result of your efforts.Mom, thank you for being strong, loving and for teaching me to believe in myself.Dad, thank you for supporting me, making awful jokes (which I laugh at from time to time), and for teaching me that life is too short not to enjoy the people we love.So thank you very much, I love you.To my siblings, Gabriela and Matheus, for being my biggest inspirations, even though I try hard not to admit it in front of you.Gabi, thank you for being the sweetest person I know (and the fiercest too!).You have the gift of making me feel welcome and comfortable.Being with you is easy.Math, thanks for getting excited about me studying something remotely close to quantum computing and genuinely believing that I'm going to get rich from it.If that happens, although it's highly unlikely, I'll dedicate part of the fortune to you.But beyond that, thank you for showing me that someone so serious and responsible can be so playful and kind.And to my brother and sister-in-law, Luc and Malu, thank you for making Gabi and Math so happy.I love you all.And Malu, thanks for Sosô.To my grandparents, Eunice, Jurandir, Victória and Olize.Abuela, know that the most important part of who I am today comes from you.Thank you for teaching me to laugh on difficult days and to look at life through the eyes of a child.Grandpa, I didn't have the privilege of knowing you, but thank you for raising this family with grandma.Vivitória, you're not here anymore either, but I'll never forget talking to you by the wood-burning stove on cold mornings in Caçador.And Grandpa, "Life is bitter enough already, isn't it?Barbarity."So I'll try to write happier things next.
Formal education is not a certified path to achieve wisdom in life.Notwithstanding, once you have the necessary support to follow it, a plethora of opportunities for selfdiscovery and edifying interactions with many inspiring minds can be found.I am deeply grateful to have the opportunity to continue developing what I believe to be one valid path, and this would not be possible without the efforts of many inspiring people that I have met, but most importantly, without the sacrifices made by my mother Simone.Consequently, this work and all of my efforts are and will always be an infinitesimal fraction of her unbelievable perseverance and braveness throughout this life.Additionally, in times upon which denialism and ignorance hinder even the possibility of human existence by normalizing abrupt and premeditated destruction of life potential, explicit gratefulness and empathy stand as a moral demonstration of character and as a necessary incentive for the exercise of living.Therefore, I would also like to acknowledge important people who were crucial to my well-being, and consequently, to this work.• To my advisor Prof. Dr. Eric de Castro e Andrade for this unique opportunity, the instigating physical discussions throughout my master's about strongly correlated systems, for the solicitous comprehension in difficult times, and for the patient and detailed orientation in each step of this dissertation.This also extends to Eric's fantastic demonstration of character in many aspects, including his concern on the future of his students.This experience was fundamental to my professional and personal development.• To Fabrizio Oliviero and Prof. Rodrigo Pereira for the opportunity to work and discuss on interesting aspects of their previous work regarding chiral spin liquids.To Prof. Eduardo Miranda and Prof. Natanael Costa for accepting our invitation to the thesis defence and for the valuable advices.• To my undergraduate thesis advisor Prof. Dr. Clovis Achy Soares Maia, who although was not directly involved in this thesis, was responsible for encouraging me to pursue a career in physics, and for writing a significant amount of recommendation letters since my undergraduate studies.Our conversations about the current status of scientific research in physics led me towards condensed matter physics, and his unique way of thinking about physics is one of the most influential professional aspects of my career.I also want to thank for equal and much important support from my undergraduate research advisor Prof. Dr. Alexandra Mocellin, who was also fundamental for this opportunity and many others.• To my mother Simone, for its incredible example of resilience, love, and will of power.It is impossible to put into words how I'm grateful for your existence and love, and although I am still stubborn in many aspects, I hope to emanate a fraction of your braveness upon each interaction within this life.Also, to my beautiful sister Luana, my good friend Ricardo and my kind-hearted old man, João Neto.Your support is the foundation and guidance for all of